Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks

Three-Dimensional Broadcasting with Optimized Transmission Ef -ficiency in Dense Wireless Net-

works

Presented by Prof. Jehn-Ruey JiangNational Central University, Taiwan

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Outline Introduction Related Work Our Solution:

• Hexagonal Prism Ring Pattern• 3D Optimized Broadcasting Protocol (3DOBP)

Performance Comparisons Conclusion

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3D wireless networks are deployed in• Multi-storey building (or warehouse)• Outer space (gravity-free factory)• Ocean (underwater sensor network)

(acoustic but not wireless) We assume the network is dense;

i.e., there are many nodes within anode’s wireless transmission area.

3D broadcasting• A source node disseminates a broadcast message

(e.g., control command or reprogramming code) to every node in the network.

Broadcasting in 3D Wireless Networks

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We’d like to apply a certain structure as the underlay.

Let’s first examine some special struc-

tures!

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Honeycomb – hexagonal lattice (grid)

Assume we’d like to use equal-radius circles to cover a plane. If the centers of circles are located at the centers of cells of a hexagonal grid, then we’ve got the minimum number of circles.

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As we are talking about 3D broadcasting, we focus on the 3D honeycomb (i.e., hexagonal grid with thickness), which consists of hexagonal prisms.

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Hexagonal Prism (8 faces)

Cube (6 faces)Rhombic Dodecahedron (12 faces)

Truncated Octahedron (14 faces)

A simple protocol for broadcasting• The source node sends out the broadcast message• Every other node rebroadcasts the message once• It is likely that every node gets the message

Drawbacks:• Broadcast storm problem (too many collisions)• Low transmission efficiency

due to a lot of redundant rebroadcast space

Flooding

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Redundant rebroadcast space

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Transmission Efficiency

The theoretical upper bound of transmission efficiency is 0.61 for the 2D plane, and 0.84 for the 3D space.

VolumnSphereNodesNumberVolumnEffectiveTE

___

COST

BENEFIT

Goal: Selecting as few as possible rebroadcast nodes to forward the message sent by the source node• to fully span all nodes in the network (coverage)• to keep all rebroadcast nodes connected (connectivity)• to achieve the optimized transmission efficiency

to save energyto reduce collisionto prolong the network lifetime

Optimized Transmission Efficiency

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Selecting 4 (out of 8) nodes to rebroadcast can span all network nodes.Is this good enough?

3D Connected Sphere Coverage Problem Transmission range of a node is assumed

as a sphere. The problem can be modeled as the

3D Connected Sphere Coverage Problem in Geometry. “How to place a minimum number of center-connected

spheres to fully cover a 3D space”

Cube

Hexagonal Prism

Truncated Octahedron

Rhombic Dodecahe-dron

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Most are Polyhedron Space-Filling Approaches:• Transmission range of a node is reduced to a polyhedron • Trying to cover (or fill) the given space with a regular arrangement

of space-filling polyhedrons (and a node at the center of a polyhedron is a rebroadcast node).

Existing Work in 3D broadcasting

Sphere CubeTransmissionRange

to fill spaceis reduced to

Space-Filling Polyhedron (1/5)

Polyhedron• is a 3D shape consisting of a finite number

of polygonal faces• E.g., cube , hexagonal prism , …

Space-Filling Polyhedron• is a polyhedron that can be used to fill a

space without any overlap or gap


Finding a space-filling polyhedronis difficult• In 350 BC, Aristotle claimed that the

tetrahedron is space-filling

• The claim was incorrect. The mistake re-mained unnoticed until the 16th century!

In 1887, Lord Kelvin asked:• “What is the optimal way to fill a 3D space

with cells of equal volume, so that the surface area between cells is minimized?”

• Kelvin’s conjecture: 14-faced truncated octahedron is the best way

Kelvin’s conjecture has not been proven yet. (Weaire–Phelan structure has a surface area 0.3% less than that of the truncated octahedron. How-ever, the structure contains two kinds of cells, ir-regular 12-faced dodecahedron and 14-faced tetrakaidecahedron.)


Lord Kelvin

Truncated Octahedron(8 hexagons + 6 squares)

Space-Filling Polyhedron (4/5) What polyhedrons can be used to fill space ?

• Cubes, Hexagonal prisms, Rhombic dodecahe-drons, and Truncated octahedrons

6-faced8-faced

Cube Hexagonal prism

Space-Filling Polyhedron (5/5) What polyhedrons can be used to fill space ?

• Cubes, Hexagonal prisms, Rhombic dodecahedrons, and Truncated octahedrons

Rhombic dodecahedrons Truncated octahedrons

14-faced12-faced

In polyhedron space-filling approaches, the transmission radius should be large enough to reach neighboring nodes, which leads to high redundancy and thus low transmission efficiency

Observation

A Btransmission radius

A Bredundant overlap region

Can we have better arrangement ?

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OUR SOLUTION:3DOBP USING

HEXAGONAL PRISM RING PATTERN

S

Top View

Source nodeCenter node

Vertex node

Hexagonal Prism Ring Pattern (1/4) The network space is divided into N layers, each of which is composed of

hexagonal prisms Layer 1 is covered by a set of rebroadcasting (forwarding) nodes

…Layer N is covered by a set of rebroadcasting (forwarding) nodes

Layer 2Layer 1

Problem: How to activate (or choose) rebroadcasting (forwarding) nodes based on the hexagonal prism ring pattern to fully cover the space in a layer?

Hexagonal Prism Ring Pattern (2/4)

Reducing spheres to hexagonal prisms• The size of hexagonal prisms is

determined by R:

Basic procedures to cover a layer of prisms:(1) Source node initially sends out the broadcast message(2) Nodes are activated to rebroadcast to form hexagonal prism rings

to cover the entire space in a layer

●

R: Transmission Radius

Initial source(center) node

L= Rඥ3/2; H= 2 Rξ3

H

L

Hexagonal Prism Ring Pattern (3/4)• To activate nodes to rebroadcast ring by ring (in 2D top view)

To activate all center nodes of hexagons via some vertex nodes of hexagons

SSS

Source Node

Activation Target Mapping .

C2,6

C1,2 C1,1

C1,0

C1,4

C2,5

C1,3

C2,3

C2,11

C2,10C2,9

C2,7

C1,5

C0,0

C2,0 C3,0

C3,1

C3,2

C3,3C3,4C3,5C3,6

C3,7

C3,8

C3,11

C3,12 C3,13 C3,14C3,15

C3,16

C3,17

Sector 0

Sector 1

Sector 2

Sector 3

Sector 4

Sector 5

A0A3

A4 A5

C3,10

C3,9

C2,8

C2,2

C2,1

S

C2,4

• The mapping is from one center node to an empty set or a set of two next-level nearest center nodes to be activated.

• q stands for the index of the 6 sectors, each of which spans 60 degrees.

• Ck,i stands for the ith center node in the ring of level k. For example, C0,0 is the source node.

• The source node activates 6 center nodes. Other center nodes activate 0 or 2 center nodes. But, a center node cannot reach a next-level center node. A vertex node located at the centroid of the three center nodes (1 Tx and 2 Rx) should help forward the message.

Geometric Mapping .

• The mapping is from one center node to a location relative to the source node s. (The source node is regarded as the origin.)

• Zk,q stands for the location relative to the source node of the hexagon center of the level-k hexagon ring on the starting axis of sector q.

starting axis of sector 0starting axis of sector 3

3DOBP : Contention Control (1) Contention Control

• Location-based contention control

Packet P < destination >2

67Sender:1. Sends a packet with the destination

of the rebroadcasting node

Receiver:2. Calculates distance from itself to destination

3. Set backoff-timer: Shorter distance Shorter backoff

4. Wait for backoff-timer to expire to rebroadcast

***The nodes with the shortest distance will rebroadcast

• If all nodes exchange their location information periodically, then a node will certainly know that itself is the node closest to the destination and can thus rebroadcast the packet at once.

3DOBP : Intralayer Activation Intralayer activation at layer t

S

S

Packet P <Vt,1,0, Vt,1,1, Vt,1,2>

SVt,1,0Vt,1,1

Vt,1,2

Packet P <Ct,1,0, Ct,1,1> Packet P <Ct,1,2, Ct,1,3>

Packet P <Ct,1,4, Ct,1,5>

3DOBP: Interlayer Activation

Layer 1

Layer -1

Layer 0

Source node (or start node S0 at layer 0)

Interlayer node I1

Start node S1 at layer 1

Interlayer node I-1

Start node S-1 at layer -1

◎

◎

◎

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Short Summary 3DOBP uses 3 major mechanisms to broadcast a

message (packet) throughout the network

(1) Contention Control(2) Intralayer Activation(3) Interlayer Activation

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Cube circumsphere

R: transmission radius

L: cube lengthRc: radius of circumsphere


Rhombic dodecahedron circumsphere

A rhombic dodecahedron can be constructed by two cubes of the length L.

Rc: radius of circumsphere

The radius Rc of the circumsphere is L. The volume RDV of a rhombic dodecahedron is 2L3.Transmision radius R=


Truncated octahedron circumsphere



L: length


Hexagonal prism circumsphere


L: length; H: height


R


3DOBP circumsphere



We assume a hexagonal prism is with side length L and height H, and that the center of each hexagonal prism is located by a node with transmission radius R.

Nc: the number of center nodes

Nv: the number of vertex nodes

L: length; H: height


3DOPB

We consider a hexagonal prism ring patter of an infinite number of levels of rings (J), and we apply the L’Hospital Rule to derive the transmission efficiency TE.

Comparisons of Transmission Efficiency


Approach Transmission Efficiency

Truncated Octahedron-based 3/8π ≈ 0.119366

Hexagonal Prism-based 3/( ) ≈ 0.168809

Rhombic Dodecahedron-based 3/( ) ≈ 0.168809

Cube-based 3/4π ≈ 0.238732

Hexagonal Prism Ring-based 1/π ≈ 0.31831

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Conclusion We introduce the 3D Optimized Broadcast Protocol

(3DOBP) using the Hexagonal Prism Ring Pattern (HPRP) to optimize the transmission efficiencyof 3D broadcasting in dense wireless networks

The protocol is the best solution so far:2D: 0.55/0.613D: 0.31/0.84

Future work: • Derive better upper bounds• Design better protocols

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Related Publication Jehn-Ruey Jiang and Tzu-Ming Sung, “Energy-Efficient Coverage and

Connectivity Maintenance for Wireless Sensor Networks,” Journal of Networks, Vol. 4, No. 6, pp. 403-410, 2009.

Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized Transmission Efficiency in Wireless Networks,” in Proc. of Fifth International Conference on Wireless and Mobile Communications, 2009.

Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized Transmission Efficiency in 3-Dimensional Wireless Networks,” in Proc. of International Conference on Parallel and Distributed Systems (ICPADS 2009), 2009.

Jehn-Ruey Jiang and Yung-Liang Lai, “Wireless Broadcasting with Optimized Transmission Efficiency,” Journal of Information Science and Engineering (JISE), Vol28, No.3, pp. 479-502, 2012.

Yung-Liang Lai and Jehn-Ruey Jiang, “A 3-dimensional broadcast protocol with optimised transmission efficiency in wireless networks,” International Journal of Ad Hoc and Ubiquitous Computing (IJAHUC), Vol. 12, Issue 4, pp. 205-215, 2013.

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Thank You!

Jiang, Jehn-RueyProfessor, NCU, Taiwan

[email protected]

Documents

Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks